Your statement is both true and misleading.

The speed of the Earth's rotation is slowing over time. Therefore leap seconds are becoming more and more common. In a century, we should be averaging something like 1 a year. In 500 years, we should be averaging one every few months. And so on.

It took over a thousand years for the Julian calendar to fall apart. Our current timekeeping system will also fall apart eventually, and I would be surprised if it lasted as long.

500 years from now, if we're still alive, enough of us will be living in space colonies rather than on the Earth's surface that the Earth's rotation will not necessarily be immediately relevant to everyone's lives.

Regardless, we've had maybe half a minute of drift since the 1970's. If the drift is 1 minute in the 2000's, 1 second per year in the 2100's, 2 seconds per year in the 2200's, 3 seconds per year in the 2300's, etc., then by 2500, the cumulative drift would add up to...60 + 100 + 200 + 300 + 400 + 500 or 1560 seconds of total cumulative drift by 2600. That's less than half an hour. If we didn't bother accounting for leap seconds, UTC midnight would be only half an hour off from astronomical midnight in 600 years, which is roughly the same error inherent in most time zones.

We need a pseudo day still due to our sleeping rhythms but perhaps people could choose that based on personal preference not just stick with 24h

The day would shift half an hour in the next 600 years. That’s half as much as it shifts twice a year for DST, except it would happen gradually over a period of time roughly equal to the time between the fall of the Eastern Roman Empire and today.

I was sort of nodding to the people who claim they have a 25 hour sleep cycle. Once we are in space and using artificial light, you can choose the sleep cycle that suits you. But predicting things in 500 year is just Sci Fi I guess!

I'm reasonably sure that any assumptions about how our anatomy will look like in 500 years are more wrong than right.

Even if there was a leap second every year... does it matter? It would still take several hundred years for the difference to be noticeable, at which point you can just change UTC by +-1h.

What it means is that the discrepancy between clocks and time of day is growing quadratically. It won't matter to us in our lifetimes. But eventually it will be a problem.

It will take on the order of a thousand years for the discrepancy to add up to an hour. In 5000 years, it will be around a day. The fact that it is currently growing about a minute per century is true, but not a good predictor of what will happen.

That said, I prefer if we just lose the astronomical basis for time keeping, and let our distant descendants figure out that they should use time zones, and not modify UTC. Hopefully by the time it becomes obvious that clocks are drifting too fast for time zones to change all of the time, we're a multi-planetary species and paying attention to what is happening on the Earth seems quaint.

In 5000 years the majority of humanity, assuming we haven’t gone extinct, will live in space and the astronomy will be moot anyway.